In this lesson, we learn about orthogonal matrices and Gram-Schmidt. An orthonormal vector and basis are introduced, and we see how having an orthogonal basis can make calculations better. Working with orthonormal vectors is useful in numerical linear algebra, as they never get out of hand. The lecture then shows how to make a given basis into an orthonormal one using the Gram-Schmidt process. Projection matrices are also discussed, and we learn that if we have an orthonormal basis, the projection matrix becomes the identity matrix. All the equations of this chapter become trivial when we have an orthonormal basis.
Orthogonal Matrices and bases, and Gram-Schmidt -- Lecture 17. Learn what an orthonormal vector and basis looks like and why it is convenient.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 22, 2008). License: Creative Commons BY-NC-SA.
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